"I was overjoyed, not least because I had not asked for it, or even expected it," the younger Mr Dunkley recalls about that first gift of a 25 per cent stake, made when the company, SLG, had just completed its first significant acquisition.
That was back in 2000, when Mr Dunkley was 33 years old, and his father, 30 years his senior, was preparing to step back from the business. It was followed by a tranche five years later that gave the younger Mr Dunkley control of the company. Mr Dunkley is now chief executive of SLG, which generates £40m in sales and employs 160 people across offices in the UK and Shanghai.
As much as 98 per cent of the world's economic activity is accounted for by family businesses but for many companies, making that transition from entrepreneurship to a smoothly-run family business is difficult, says Allan Cohen, a professor in global leadership at Babson College, a US business school that specialises in entrepreneurship research.
"When a business has been built from scratch, many entrepreneurs have difficulty letting go of running it, whether to experienced executives or their own children," he says.
That transition is made particularly difficult when the family member to whom the founder wants to pass the business is young. Founding a company is often seen as more exciting than inheriting a parent's creation, according to Shaheena Janjuha Jivraj, a senior lecturer at Henley Business School, who has been researching family businesses for the last two decades.
The transfer of power is easier when there is a clear successor as in the case of SLG. When there are multiple children, the risk is that someone feels left out, notes Bernard Rennell, global head of family governance and enterprise succession at HSBC.
"It can be a worrying time for founders as they need to ensure the outcome is good for the family as well as for the business," he says.
David Glassman, a visiting fellow at Cranfield School of Management, who coaches chief executives and advises on family business issues, says the key is to avoid favouritism or any perception of it.
"Apply clear performance measures to all roles and monitor them for the sake of all," Mr Glassman says. "This process, used judiciously, will spread a clear message of meritocracy to current and future employees."
However, Prof Cohen points out that it can be difficult for a founder entrepreneur to acknowledge the merits of a former dependent.
Mr Dunkley was able to show his father his worth because he had been working as a senior executive in the business for several years when his father gave him his first stake in the company. "I was hungry to take risk, and power the company ahead, and my father was understandably winding down," Mr Dunkley says.
The handover of the second, majority stake followed a surge in growth at SLG helped both by an acquisition and strategies the younger Mr Dunkley had introduced. That improvement in the company's fortunes helped smooth the transfer of control.
Money is the root of many transfer problems, says Prof Cohen. "If the company is seen as the source of the family's financial future, the concerns can be magnified about whether the family member is competent to protect that," he says.
As a father of three children, Mr Dunkley has the capacity to hand SLG on to the next generation, although the eldest is only 16 so the decision is not imminent. Mr Dunkley is also far from certain whether he wants SLG to pass to a third generation of the family.
He says the decision will be decided by the head rather than the heart. "I've seen many cases where the pre-determined family succession plan doesn't work and nobody wants that," he notes.
Mr Dunkley reminds himself of his good fortune by keeping framed in his home office a greetings card from his father at the time of the handover of power. It is full of words of encouragement, Mr Dunkley says. "I regard myself as lucky, because from day one my dad had tremendous faith in me," a faith he has so far justified by ensuring he "did not mess things up".